LP models for bin packing and cutting stock problems |
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| Institution: | 1. Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Office C216, Viña del Mar, Chile;2. Escola Universitària d’Enginyeria Tècnica Industrial de Barcelona, Universitat Politècnica de Catalunya, C. Comte Urgell, 187 1st. Floor, 08036 Barcelona, Spain;1. IDOM Consulting, Engineering, Architecture, Spain;2. Department of Computer Science, Computer Architecture, Computer Languages & Information Systems, Statistics & Operations Research, Universidad Rey Juan Carlos, Spain;3. Departamento de Estadística e Investigación Operativa, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Spain;1. School of Information Technology, Deakin University, Geelong 3216, Australia;2. Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait;1. School of Management, University of Bath, Claverton Down, Bath BA2 7AY, UK;2. Department of Industrial Engineering, Bahçeşehir University, Çırağan Cad. No:4 Beşiktaş, Istanbul 34353, Turkey |
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| Abstract: | We review several linear programming (LP) formulations for the one-dimensional cutting stock and bin packing problems, namely, the models of Kantorovich, Gilmore–Gomory, onecut models, as in the Dyckhoff–Stadtler approach, position-indexed models, and a model derived from the vehicle routing literature.We analyse some relations between the corresponding LP relaxations, and their relative strengths, and refer how to derive branching schemes that can be used in the exact solution of these problems, using branch-and-price. |
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